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On fundamental problems with calculus

I fully agree that "calculus" is a deeply troubled theory of mathematics,which lead to the more troubled theory of mathematics called topologywhich ended up with a largest play ground for "problem solvers" toenumerate problems and publish papers endlessly.Going back to the calculus, historically it is false that this wasdeveloped by Newton and Leibniz. About three hundred years before it wasdeveloped in India. They did not use it for building Physics. They justwanted to build a mathematical model of celestial system to be used foragriculture. I do not know if these two developments are independent.The issue in Calculus a la Europe is that it was impossible to define theconcept of "limit" articulately. It took about two centuries for European(mostly German) mathematicians to gain this concept properly using thetheory of complete ordered field and epsilon-delta argument. This approachdeveloped into general topology from which the so called algebraictopology came out.It was unfortunate that this method though worked fine had little to dowith the original calculus used in early physics in which naive concept ofinfinitesimals were used. In fact, the topological calculus was developedas an anti-thesis to the infinitesimal based calculus. This is what moststudent learns in the university. Rarely infinitesimal caluclus is taughtthought we have modern and complete infinitesimal calculus as developed byAbraham Robinson in 1960. The reason for all of this is because the naiveconcept of infinitesimals is apparently paradoxical as even George Cantorcomplained. Certainly it is trouble some to figure out what kind ofnumbers are "positive numbers each of which is smaller than all positivereal numbers".Robinson was a most important mathematical logician (model theorist) inthe history of mathematics though due to the advanced and difficult natureof his work, it went over the head of popular scientists and did not getappreciation which so badly deserved. It is my view that this had a lot todo with the anti-logic culture of theoretical physics. As you know well,logic was developed to very high level by the Scholastic Philosophers inVatican who wanted to prove that God exists. Unlike Physicists, they werequite open and honest. They realized that in all of their proofs for theexistence of God, they assumed the existence of God in one way or theother. So, they said predicate logic will not do. This lead them to thedevelopment of modal logic in which they tried to prove the necessity ofGod instead of existence. As the bloody history of theoretical physicsproves, basically admitting the error and defeat is the last thing for theKing of science would do. This ended up with the situation where evensecondary school students become highly critical of this entire activity.The final outcome is that the King of Science left this ugly expensiveCERN and highly questionable authority to dominate at any cost. Notwithstanding, as a professional logician, I can tell you that welogicians are still learning from the Vatican cosmology, though we learnedvery little from the so called theoretical physics. The problem is thatall we see in theoretical physics as we know of now looks nothing but amountain of errors and deceptions created by earthly expectations. Afterall, to be fair, we logicians learned from QM as the development ofquantum logic. This strangest logic became a fashion for a decade or so,long time ago and nobody even remembers.Anyhow, regarding QM, it is a very good example of how logically inconsistent theory whose inconsistency is well concealed by the politicsof intimidation, black mailing and name calling can create total illusionand thrive as "science fiction" as exactly happening now.So, going back to infinitesimal calculus of Robinson. To be honest only very strong experts in mathematical logic can follow what he did. Itstarts with a strange theory of the first order real numbers. This isneeded as we define infinitesimal calculus as the nonstandard model of thefirst order calculus, taking advantage of the weakness of the first ordertheory. Using fully developed model theory (to its development Robinsonwas a major contributor), using the ultra power construction andcollapsing it to quotient structure using the provable equality of thefirst order real number theory, he obtained full infinitesimal calculus.In easier language, as we define real numbers as infinite sequences ofrational numbers separating rationals and irrationals represented asinfinite sequences of rationals, Robinson considered infinite sequencesof real numbers as nonstandard real numbers and separated those whichconverges and which do not as real numbers and infinity. As the reciprocalof infinity he defined infinitesimals.After all of this basically without using limit, we can develop fullcalculus. Limitless calculus meant topology-less calculus. Indeed thetopology of infinitesimal calculus is trivial T0 topology.I think one of the reason why Robinson was never appreciated in mainstreammathematics community has a lot to do with the pressure from the communityof mathematical physicists who felt threatened by his work which willmake their work unnecessary complication. After fleeing from Nazipersecution, he fled to Israel and then came to Canada. He became a memberof mathematics department at U of Toronto. Despite his great work, he wasnot appreciated and so he moved to UC Irvin to chair the math departmentand shortly after that he died young by cancer. The sad fact is that henever worked for places like Stanford or Harvard.However, we do have some problem with Robinson's infinitesimal calculus.His infinitesimals have little to do with what Leibniz and Newton meant.Physical interpretation of Robinson's infinitesimals is not as obvious asit should be. I learned that there are some other infinitesimal calculusdeveloped after Robinson. But, I do not think any of them are as powerfulas Robinson's and have any better fit with infinitesimals physics needs. For example I do not see how we can associate a fixed charge for amathematical infinitesimal. This is a common way to use infinitesimals inPhysics.What is tragic is that due to the specialization and stupid ego trips, thecommunication between physics and pure mathematicians ceased to exist.Despite this concern, I am already a senior citizen and have not much timeleft. So, I hope young researchers will take up this kind of veryfundamental problems for the advancement of science.AK

What God promised to tell me to do as the Elijah for the End of Times.

*And now He fulfill His promise, because this is the end of Times.

Note: Believe it or not, this article was written very carefully under guidance of Holy Spirit, because I do not know the meaning and unprepared to become a prophet of God. But thanks God, He is full of mercy.

Beginning
God call me in Oct. 2009 as His prophet in order to prepare so many people in His body of churches and nations for the End of Times. Before that, God asked me three times: "Do you love Me? Then shepherd My lambs." And I replied, "Yes, God. You know that I love You." At the time, I remembered that classic conversation between Jesus and Peter in John chapter 21. I tried to see how the relation of Jesus's question to Peter and God's question to me, but it is mystery.
Initially, I was so enthusiastic with this unexpected job from God to become His prophet, and at the time, a part of me said that it is a very …

Drink the new wine (2014)

A.L.I.C.E with Jesus

Mengenai Saya

He was born in Indonesia, and studied engineering in a state university in East Java. Then he worked until 2008. In Dec. 2008 he was granted a scholarship to study gravitation and cosmology at Institute of Gravitation and Cosmology in Moscow until June 2009. Since Oct. 2009, he works for Jesus Christ. He published more than 45 papers and 16 books. Get his new book: https://www.facebook.com/ABiblicalTheoryofEverything.
Since Aug. 2015, he holds Doctorate of Divinity and administers Sci4God.com.